Is it only Aikido if it comes from Ueshiba???
I'm inclined to say no. All aikido is not Ueshiba ryu. Too many other people have come the a similar point with out Ueshiba's help.
As to Tohei being asked not to use the term Aikido. From all that I have read and from the folks here in Hawaii that I've talked to who were around at the time of the break up there was a lot of nastiness at that time. The Ueshiba's desire for "ownership" of the term "Aikido may have stemed from that.
While Aikikai (and to some extent Tohei) aikido may be about polishing the mirror not all aikido is I'm fairly sure that NGA is much more about self defence than mirror polishing. I doubt the Yosh folks would agree with the mirror polish comment either. Many people like Aikido for its effectiveness and could care less about its spiritual side. That doesn't make them wrong just different than you. Aiki just is...you either accept it or lose to it